As far as displaying data from another database goes the first thing would be to have a content part or a widget defined. On the Display method of the ContentPartDriver you should connect to the other database, and query for whatever data you need.

By "ASP.NET" you could mean either MVC or Webforms - they're two different technologies within the ASP.NET framework. Orchard runs on MVC and so Webforms isn't supported in any views, doesn't matter where they're coming from. Widgets are just content items
with a special setting.

You should start by reading some of the tutorials on orchardproject.net, they'll walk you through creating a basic module and a Content Part, which is a way of extending any content item with your own logic and templates: